David A. Edwards

Professor of Mathematics

Department of Mathematical Sciences

University of Delaware

Newark, DE 19716-2553

(302) 831-1871

`https://sites.udel.edu/dedwards`

(This page contains my most recent accomplishments. For information on older accomplishments, as well as some other supplemental information, click here.)

Jump ahead to Service, Journal Publications, or Other Publications.

**Graduate:**- California Institute of Technology, Pasadena, California
- Ph.D. (Applied Mathematics), 1994
- Thesis Title:
*A Model for Nonlinear Diffusion in Polymers* - Thesis Advisor: Donald S. Cohen
**Undergraduate:**- California Institute of Technology, Pasadena, California
- B.S. with Honor (Applied Mathematics), 1990
**Actuarial Science:**- 2004 System: Passed Exams P, MF, M, and all VEE
- 1990s System: Passed Exams 100, 110, 120, 130, 135, 140, 150, 151

**September 2007-present**-
- Professor
- Department of Mathematical Sciences
- University of Delaware
- Newark, Delaware
- Pursue interesting questions in biochemical reactions, electrogenerated chemiluminescence waves, neural signaling in the olfactory system, solar cells, mathematical finance, box office dynamics, 3-D printing, and transport in foams. Teach (undergraduate) Differential Equations with Linear Algebra I and II, Elementary Linear Algebra, Engineering Mathematics I, Ordinary Differential Equations, Application of Mathematics in Economics, Introduction to Partial Differential Equations and (graduate) Introduction to Applied Mathematics I and II, Vector Spaces, Asymptotics and Perturbation Methods, and Introduction to Mathematical Finance.

**September 2010-August 2011**-
- Interim Chair
- Department of Mathematical Sciences
- University of Delaware
- Newark, Delaware
- Led a department of over 50 full-time faculty and staff. Responsible for faculty and personnel development, program development and departmental planning, and budgetary functions.

**March 1999-present**-
- Consultant
- Jones Day
- Washington, District of Columbia
- Analyze the validity of mathematical models presented as evidence in litigation. Perform statistical analysis of various data introduced in litigation.

**September 2005-August 2010**-
- Associate Chair
- Department of Mathematical Sciences
- University of Delaware
- Newark, Delaware
- Had primary responsibility for most teaching-related functions of the department. Responsible for course scheduling and instructor assignment for mathematical sciences courses. Served as complaint resolution official. Approved transfers of credit and grade changes. Supervised some instructional personnel.

**September 2001-August 2007**-
- Associate Professor
- Department of Mathematical Sciences
- University of Delaware
- Newark, Delaware
- Pursued interesting questions in mathematical finance, neural signaling in the olfactory system, and biological bimolecular reactions. Also did modeling research in polymer skinning. Taught (undergraduate) Analytic Geometry and Calculus A, Ordinary Differential Equations, Differential Equations with Linear Algebra I, and (graduate) Asymptotics and Perturbation Methods, Vector Spaces, and Introduction to Applied Mathematics I and II.

**September 1997-August 2001**-
- Assistant Professor
- Department of Mathematical Sciences
- University of Delaware
- Newark, Delaware
- Pursued research in polymers, biological bimolecular reactions, shear band formation, and box office dynamics. Teach (undergraduate) Analytic Geometry and Calculus A and C, Elementary Linear Algebra, Differential Equations with Linear Algebra I and II, and (graduate) Topics in Differential and Integral Equations and Introduction to Applied Mathematics I and II.

**August 1995-July 1997**-
- Visiting Assistant Professor/NSF Research Instructor
- Department of Mathematics
- University of Maryland, College Park
- College Park, Maryland
- Pursued interesting questions related to my thesis research in polymers and explore new avenues of investigation, including viscoelastic rod dynamics, shear band formation, and biological bimolecular reactions. Taught (undergraduate) Introduction to Linear Algebra and (undergraduate/graduate) Methods and Models in Applied Mathematics II.

**September 1994-August 1995**-
- Assistant Professor of Mathematics/Courant Instructor/ NSF Research Instructor
- Courant Institute of Mathematical Sciences
- New York University
- New York, New York
- Pursued interesting questions related to my thesis research in polymers and explored new avenues of investigation, including Prandtl boundary-layer flow. Taught (undergraduate) Calculus I and (graduate) Linear Algebra II.

**Research:**- National Science Foundation, 2013-2017
- National Institutes of Health, 2002-07 (subcontract PI; PI: Paul Milewski)
- National Science Foundation, 1999-2002
- University of Delaware Research Foundation, 1999-2001
**Workshops:**- National Science Foundation, Support of the Sixteenth Annual Gradute Student Mathematical Modeling Camp, 2020-present (PI)
- National Science Foundation, Support of the Fifteenth Annual Gradute Student Mathematical Modeling Camp, 2019-present (PI)
- Institute for Mathematics and Its Applications, Support of the Fifteenth and Sixteenth Annual Gradute Student Mathematical Modeling Camp, 2019-present (co-PI)
- National Science Foundation, Support of the Twenty-Ninth through Thirty-Fifth Annual Workshop on Problems in Industry, 2013-2019 (co-PI)
- National Science Foundation, Support of the Twenty-Eighth Annual Workshop on Problems in Industry, 2012 (co-PI)

Institute for Mathematics and Its Applications, Support of the Twenty-Eighth Annual Workshop on Problems in Industry, 2012 (co-PI) - Institute for Mathematics and Its Applications, Support of the Twenty-Third Annual Workshop on Problems in Industry, 2007 (co-PI)
- Institute for Mathematics and Its Applications, Support of the Twentieth Annual Workshop on Problems in Industry, 2004 (co-PI)
- National Institute for Standards and Technology, Support of the Sixteenth Annual Workshop on Problems in Industry, 2000 (PI: Richard Braun)
- National Institute for Standards and Technology, Support of the Fifteenth Annual Workshop on Problems in Industry, 1999 (PI: Richard Braun)
**Postdoctoral:**- National Science Foundation Postdoctoral Research Instructor, 1994-97
**Graduate:**- Hertz Foundation Fellow, 1993-94
- National Science Foundation Graduate Fellow, 1990-93

**Invited Presentations:**- Toyota-UD Applied Math Initiative Workshop for High School Teachers, University of Delaware, July 2014
- Department of Mathematical Sciences, New Jersey Institute of Technology, October 2012
- Conference on Applied Analysis and Mathematical Biology, University of Delaware, August 2012
- Degenerate Reaction-Diffusion Equations Arising in Polymer Diffusion and Their Connection to Problems in Mathematical Biology (2 talks), Brunel University, July 2008
- The Legacy of John Crank: Developments in Time Dependent PDEs, Diffusion and Free Boundary Problems, Brunel University, July 2008
- Department of Mathematics and Statistics, University of Maryland, Baltimore County, April 2008
- Department of Mathematical Sciences, New Jersey Institute of Technology, November 2004
- Mathematical Biosciences Institute, Ohio State University, October 2004
- Department of Mathematics and Statistics, University of Maryland, Baltimore County, September 2004 (colloquium)
- Department of Mechanical Engineering and Applied Mechanics , University of Pennsylvania, September 2002
- Department of Mathematics , University of Wisconsin, Madison, October 2001
- Department of Mathematics and Statistics, University of Maryland, Baltimore County, October 2000
- Biosensor Core Facility, University of Pennsylvania, September 2000
- School of Mathematics, Georgia Institute of Technology, January 2000
- Department of Mathematical Sciences, University of Delaware, April 1999 (Math Awareness Month public lecture)
- Department of Mathematics and Statistics, University of Nebraska, January 1999 (colloquium)
- Department of Mathematical Sciences, New Jersey Institute of Technology, September 1998
- Department of Chemical Engineering, Drexel University, February 1998
- Department of Mathematical Sciences, University of Cincinnati, May 1997
- Department of Mathematics and Statistics, University of Maryland, Baltimore County, September 1996
**Minisymposia:**- SIAM Conference on Applied Mathematics Education, Pittsburgh, July 2022
- AMS Sectional Meeting #1098, Catonsville, MD, March 2014
- SIAM Annual Meeting, Denver, July 2009
- SIAM Conference on Mathematics for Industry: Challenges and Frontiers, Philadelphia, October 2007
- Joint SIAM-SMB Conference on the Life Sciences, Raleigh, August 2006 (co-organizer)
- SIAM Annual Meeting, New Orleans, July 2005 (co-organizer)
- AMS Sectional Meeting #1005, Newark, DE, April 2005 (session organizer and additional paper)
- Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Blacksburg, June 2002
- SIAM Annual Meeting , San Diego, July 2001 (co-organizer)
- SIAM Annual Meeting, Philadelphia, July 1993
**Contributed Papers:**- SIAM Conference on Financial Mathematics & Engineering, Toronto, July 2019
- SIAM Annual Meeting, Boston, July 2016
- SMB Annual Meeting, Atlanta, July 2015
- SIAM Annual Meeting, Pittsburgh, July 2010
- SIAM Annual Meeting, San Diego, July 2001
- SIAM Annual Meeting, Puerto Rico, July 2000
- Nonlinear Analysis 2000–>, New York, May 2000 (poster presentation)
- Third SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia, May 2000
- BIAsymposium, San Francisco, November 1999 (poster presentation)
- SIAM Annual Meeting, Toronto, July 1998 (two papers: talk 1, talk 2)
- Ninth International Coating Science and Technology Symposium, Newark, DE, May 1998 (proceedings published; see [
**O10**]) - SIAM Annual Meeting, Kansas City, July 1996 (session chair)
- AIChE Annual Meeting, San Francisco, November 1994
- SIAM Annual Meeting, San Diego, July 1994

**Workshops resulting in reports:**-
- Thirty-Eighth Workshop on Mathematical Problems in Industry, Worcester, MA, June 2022
- (organizing committee)
- Thirty-Seventh Workshop on Mathematical Problems in Industry, June 2021
- (organizing committee; proceedings published; see [
**O33**]) - Thirty-Sixth Workshop on Mathematical Problems in Industry, June 2020
- (organizing committee; proceedings published; see [
**O32**]) - Thirty-Fifth Workshop on Mathematical Problems in Industry, Newark, NJ, June 2019
- (organizing committee; proceedings published; see [
**O31**] and [**O35**]) - Thirty-Fourth Workshop on Mathematical Problems in Industry, Claremont, CA, June 2018
- (organizing committee; proceedings published; see [
**O30**]) - Thirty-Third Workshop on Mathematical Problems in Industry, Newark, NJ, June 2017
- (organizing committee; proceedings published; see [
**O29**]) - Thirty-Second Workshop on Mathematical Problems in Industry, Durham, NC, June 2016
- (organizing committee; proceedings published; see [
**O28**]) - Thirty-First Annual Workshop on Problems in Industry, Newark, DE, June 2015
- (organizing committee; proceedings published; see [
**O27**]) - Thirtieth Annual Workshop on Problems in Industry, Newark, NJ, June 2014
- (organizing committee; proceedings published; see [
**O26**]) - Twenty-Ninth Annual Workshop on Problems in Industry, Worcester, MA, June 2013
- (organizing committee; proceedings published; see [
**O25**]) - Pall Corporation Industrial Study Group, Portsmouth, UK, March 2013
- Twenty-Eighth Annual Workshop on Problems in Industry, Newark, DE, June 2012
- (organizing committee; proceedings published; see [
**O24**]) - Twenty-Seventh Annual Workshop on Problems in Industry, Newark, NJ, June 2011
- (proceedings published; see [
**O23**]) - Twenty-Sixth Annual Workshop on Problems in Industry, Troy, NY, June 2010
- (proceedings published; see [
**O22**]) - Twenty-Fifth Annual Workshop on Problems in Industry, Newark, DE, June 2009
- (organizing committee, proceedings published; see [
**O21**]) - Twenty-Third Annual Workshop on Problems in Industry, Newark, DE, June 2007
- (organizing committee, proceedings published; see [
**O20**]) - Twenty-Second Annual Workshop on Problems in Industry, Needham, MA, June 2006
- (organizing committee, proceedings published; see [
**O19**]) - Twenty-First Annual Workshop on Problems in Industry, Worcester, MA, June 2005
- (proceedings published; see [
**O18**]) - Twentieth Annual Workshop on Problems in Industry, Newark. DE, June 2004
- (organizing committee; proceedings published; see [
**O17**]) - Seventeenth Annual Workshop on Problems in Industry, Troy, NY, June 2001
- (proceedings published; see [
**O14**]) - Sixteenth Annual Workshop on Problems in Industry, Newark, DE, June 2000
- (organizing committee; proceedings published; see [
**O13**]) - Fifteenth Annual Workshop on Problems in Industry, Newark, DE, June 1999
- (organizing committee; proceedings published; see [
**O12**]) - Fourteenth Annual Workshop on Problems in Industry, Troy, NY, June 1998
- (proceedings published; see [
**O11**]) - Thirteenth Annual Workshop on Problems in Industry, Troy, NY, June 1997
- (proceedings published; see [
**O9**]) - Twelfth Annual Workshop on Problems in Industry, Troy, NY, June 1996
- (proceedings published; see [
**O8**]) - Eleventh Annual Workshop on Problems in Industry, Albuquerque, NM, June 1995
- (proceedings published; see [
**O6**])

**Graduate Research:**- Alexandra Vasconez-Moncayo, Summer 2020
- Avishek Mukherjee, Summer 2018
- Ryan Evans, “A Mathematical Journey Through Optical Biosensors,” 2014-2016
- Nicholas Kaufman, Summer 2014
- Matt Zumbrum, “Extensions for a Surface-Volume Reaction Model with Application to Optical Biosensors,” 2010-13
- Qinghua Zhu, “Pricing Exchange Options with Stochastic Correlations,” 2006-10
- Amit Samant (co-advisor with Gilberto Schleiniger), 2002-04
**Undergraduate Research:**-
- Jacob Sitison, “3-D Printing Extrusion Rates Through a Tapered Nozzle,” Summer 2019-Spring 2020 (thesis)
- (manuscript published; see [
**J59**]) - Ryan Talley-McGovern, “Modeling Transport Effects in BIAcore Reactions”, Summer 2018
- Lucas Onisk, “Multi-Site Reaction Rate Constant Evaluation”, Summer 2017
- Wenbin Li, Summer 2015-2016
- Alyson Grassi, “Modeling Multicomponent Reactions Through the Use of Ordinary Differential Equations”, Summer 2014
- Jessica Shearer, “Multicomponent Reactions in the BIAcore”, Summer 2013
- Linsey Norris, “Continuing Numerical Modeling for the Receptor Layer in the BIAcore,” Summer 2006
- Ken Bell, “A Numerical Model for the Receptor Layer in the BIAcore,” Summer 2004
- Sumanth Swaminathan, “A Mathematical Model of Blood Clotting,” Summer 2003-Winter 2004
- (results published; see [
**O16**]) - Sumanth Swaminathan, “Effects of Small Receptor Density Variation in the BIAcore,” Winter 2003
- (results published; see [
**J26**]) - Sumanth Swaminathan, “Traveling Wave Solutions of Nonlinear Diffusion Equations,” Summer 2002
- (results published; see [
**J24**]) - Nate Allen, “The Effects of a Receptor Layer in the BIAcore Device,” Summer 2001
- Seth Jackson, “A Nonlinear Integral Equation Arising in the IAsys Device,” Summer 2000
- (manuscript published; see [
**O15**]) - Seth Jackson, “A Nonlinear Integral Equation Arising in Biochemical Systems,” Summer 1999
- (manuscript published; see [
**J22**])

**University Related:**- MATH Graduate Mentor, 2020-present
- MSDS Graduate Advisor, 2020-present
- MATH Undergraduate Advisor, 1997-2005

**Computer Skills:**- Extensive classroom implementation of numerical analysis techniques, including finite difference methods, iterative solvers, finite element techniques, multigrid, and spectral methods on ordinary and partial differential equations of all types.
- Extensive knowledge of Maple, Mathematica, Matlab, and TEX.
- Good working knowledge of C, C++, Canvas, HTML, LaTEX, and Qualtrics.
- Extensive knowledge of Macintosh operating system.
- Good working knowledge of UNIX and Microsoft Windows operating systems.
- Familiarity with Linux operating system.
**Languages:**- Excellent French reading comprehension and writing skills.
- Acceptable French oral communication skills.

**Major Duties:**- Interim Chair, 2010-2011
- Associate Chair, 2005-2010, 2022-present
*Ex officio*member, Advisory Committee, 2005-2011, 2022-present- Member, Graduate Committee: Spring 2001, 2013-17, 2020-21
- Member, Math Alliance: 2020-present
- Graduate Student Mentor: 2020-present
- Co-Chair,
*Ad Hoc*CT Priorities Committee, 2021-2022 - Organizer, Departmental Math Awareness Month Activities, 2003-04, 2006
- Chair, Outreach Committee: 2002, Spring/Summer 2004
- Chair, Colloquium Committee: 1998-99
- Secretary, Promotion and Tenure Committee: 2015-16, 2018-19
- Member, Promotion and Tenure Committee: 2001-present
- Chair, Peer Review Committee: 2013, 2016-19
- Member, Peer Review Committee: 2008, 2012
- Undergraduate Research Coordinator, 2012-13
- Member, Undergraduate Studies Committee: 1999-2000, 2001-02, 2012-13, 2017-18
- Member, Convocation Committee: 1998-99, 2000-01, 2002-05
- Member, Computer Technology Committee: 1999-2001
- Member, Colloquium Committee: 1997-98
**Examination Committees:**- Chair, Applied Math Candidacy Exam Committee: Winter 2002
- Member, Dissertation Defense Committee: 2000, 2003, 2006 (MEEG), 2013, 2018
- Member, Linear Algebra Preliminary Exam Committee: 2002-06, 2009, 2014, 2017, 2018
- Member, Applied Math Candidacy Exam Committee: 2000-01, 2011, 2013, 2014
- Member, PDE Candidacy Exam Committee: 1999
- French Examiner: 1999
**Course Coordinator/Leader for:**- Mathematics 351: Fall 2022
- Mathematics 302: Fall 2002
- Mathematics 241: Fall 1998, Fall 2001, Spring 2002
**Search Committees:**- Search Committee Chair: 2014-15 (tenure track), 2021-22 (continuing track)
- Actuarial Sciences Search Committee, 2022–present
- Opportunity Search Committee: 2014
- UNIDEL Postdoctoral Search Committee: 2005-10
- Probability/Topology Search Committee, 2003-04
- Applied Mathematics Search Committee: 2001-02
- Temporary Assistant Professor Search Committee: 2000-01
**Other Duties:**- Department Marshal, Commencement Exercises: 1998-2005, 2007-2011, 2013-present
- ACSC Recruiting Video, 2021
- Math Circles Presenter, 2013
- Co-Organizer, Applied Math Seminar: Spring 2001

**College:**- Chair, Peer Review Committee, 2009
- Secretary of College Senate, 2006-07
- Nominee, President-Elect of College Senate, 2005
- Member, College Biotech Research Council, 2001-02
**University:**- Nominee, Outstanding RSO Advisor, 2018
- Advisor, Actuarial Sciences Club, 2015–present
- Nominee, Excellence in Undergraduate Academic Advising and Mentoring, 2016
- Member, Council on Pre-Collegiate Programs, 2007
- Nominee, Excellence in Teaching Award, 2003
**Disciplinary:**- Member, Organizing Committee, Thirty-Eighth Workshop on Mathematical Problems in Industry, 2022
- Co-Director, Sixteenth Annual Graduate Student Mathematical Modeling Camp, 2022
- Member, Organizing Committee, Thirty-Seventh Workshop on Mathematical Problems in Industry, 2021
- Co-Director, Sixteenth Annual Graduate Student Mathematical Modeling Camp, 2021
- Member, Organizing Committee, Thirty-Sixth Workshop on Mathematical Problems in Industry, 2020
- Co-Director, Fifteenth Annual Graduate Student Mathematical Modeling Camp, 2019
- Member, Organizing Committee, Thirty-Fifth Workshop on Mathematical Problems in Industry, 2019
- Member, Organizing Committee, Thirty-Fourth Workshop on Mathematical Problems in Industry, 2018
- Member, Organizing Committee, Thirty-Third Workshop on Mathematical Problems in Industry, 2017
- Member, Organizing Committee, Thirty-Second Workshop on Mathematical Problems in Industry, 2016
- Member, Organizing Committee, Thirty-First Annual Workshop on Problems in Industry, 2015
- Member, Organizing Committee, Thirtieth Annual Workshop on Problems in Industry, 2014
- Member, Organizing Committee, Twenty-Ninth Annual Workshop on Problems in Industry, 2013
- Member, Organizing Committee, Twenty-Eighth Annual Workshop on Problems in Industry, 2012
- Member, Organizing Committee, Twenty-Fifth Annual Workshop on Problems in Industry, 2009
- Member, Organizing Committee, Twenty-Fourth Annual Workshop on Problems in Industry, 2008
- Member, Organizing Committee, Twenty-Third Annual Workshop on Problems in Industry, 2007
- Member, Organizing Committee, Twenty-Second Annual Workshop on Problems in Industry, 2006
- Member, Organizing Committee, Twentieth Annual Workshop on Problems in Industry, 2004
- Member, Organizing Committee, Sixteenth Annual Workshop on Problems in Industry, 2000
- Member, Organizing Committee, Fifteenth Annual Workshop on Problems in Industry, 1999
**University Affiliations:**- Delaware Biotechnology Institute
- Institute for Financial Services Analytics
**Professional Affiliations:**- SIAM
**Reviewer for:**-
- Biological Journals
*Biometrical Journal**Biophysical Journal**European Biophysics Journal**Journal of Mathematical Biology**Journal of Theoretical Biology**Mathematical Biosciences**Mathematical Medicine and Biology*- Business Journals
*Computational Economics**Quantitative Finance*- Engineering and Science Journals
*AIChE Journal**The European Physical Journal Plus**IEEE Sensors Journal**Journal of Applied Polymer Science**Journal of Heat Transfer**Journal of Polymer Science Part B: Polymer Physics**Journal of Rheology**Macromolecular Theory and Simulations**Physica A*- General Interest Journals
*Scientific Reports**UMBC Review*- Mathematics Journals
*Applicable Analysis**Applied Mathematics Letters**Computers, Materials, and Continua**European Journal of Applied Mathematics**International Journal of Mathematics and Mathematical Sciences**Journal of Engineering Mathematics**Journal of Mathematical and Physical Sciences**Mathematical and Computer Modelling**Mathematical Methods in the Applied Sciences**Mathematical Modelling and Numerical Analysis**Mathematical Reviews**Numerical Methods for Partial Differential Equations**SIAM Journal on Applied Mathematics**SIAM Review*(manuscripts and books)*SIAM Undergraduate Research Online**Studies in Applied Mathematics**ZAMP*

- Addison-Wesley Longman Publishing
- Arkansas Science and Technology Authority
- Mathematics of Information Technology and Complex Systems
- National Science Foundation
- Petroleum Research Fund
- Prentice-Hall Publishing
- Springer-Verlag Publishing
- promotion and tenure consideration (external)
**Other:**- Web-page design for non-profit corporation

- [
**J1**] - “An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems.”
*SIAM Journal on Applied Mathematics*,**55**(1995): 662-676 (with Donald S. Cohen). - [
**J2**] - “Constant Front Speed in Weakly Diffusive Non-Fickian Systems.”
*SIAM Journal on Applied Mathematics*,**55**(1995): 1039-1058. - [
**J3**] - “The Effect of a Changing Diffusion Coefficient in Super-Case II Polymer- Penetrant Systems.”
*IMA Journal of Applied Mathematics*,**55**(1995): 49-66 (with Donald S. Cohen). - [
**J4**] - “A Mathematical Model for a Dissolving Polymer.”
*AIChE Journal*,**41**(1995): 2345-2355 (with Donald S. Cohen). - [
**J5**] - “Non-Fickian Diffusion in Thin Polymer Films.”
*Journal of Polymer Science, Part B: Polymer Physics Edition*,**34**(1996): 981-997. - [
**J6**] - “Perturbation Analysis of Thomas’ and Windle’s Model of Case II Transport.”
*AIChE Journal*,**42**(1996): 2025-2035 (with Christopher J. Durning and Donald S. Cohen). - [
**J7**] - “Viscous Boundary-Layer Effects in Nearly Inviscid Cylindrical Flows.”
*Nonlinearity*,**10**(1997): 277-290. - [
**J8**] - “Trace Element Disequilibria and Magnesium Isotope Heterogeneity in 3655A: Evidence for a Complex Multi-Stage Evolution of a Typical Allende Type B1 CAI.”
*Geochimica et Cosmochimica Acta*,**61**(1997): 1541-1561 (with Allen K. Kennedy*et al*.). - [
**J9**] - “A Mathematical Model for Trapping Skinning in Polymers.”
*Studies in Applied Mathematics*,**99**(1997): 49-80. - [
**J10**] - “Trapping Skinning in Polymers: Theoretical Predictions.”
*Chemical Engineering Communications*,**166**(1998): 201-216. - [
**J11**] - “Asymptotic and Computational Analysis of Large Shear Deformations of a Thermoplastic Material.”
*SIAM Journal on Applied Mathematics*,**59**(1998): 700-24 (with Donald A. French). - [
**J12**] - “An Asymptotic Analysis of Polymer Desorption and Skinning.”
*Macromolecular Theory and Simulations*,**8**(1999): 10-14. - [
**J13**] - “Skinning During Desorption of Polymers: An Asymptotic Analysis.”
*SIAM Journal on Applied Mathematics*,**59**(1999): 1134-1155. - [
**J14**] - “Estimating Rate Constants in a Convection-Diffusion System with a Boundary Reaction.”
*IMA Journal of Applied Mathematics*,**63**(1999): 89-112. - [
**J15**] - “Transport Effects on Surface-Volume Biological Reactions.”
*Journal of Mathematical Biology*,**39**(1999): 533-561 (with Byron Goldstein and Donald S. Cohen). - [
**J16**] - “Biochemical Reactions on Helical Structures.”
*SIAM Journal on Applied Mathematics*,**60**(2000): 1425-1446. - [
**J17**] - “An Alternative Example of the Method of Multiple Scales.”
*SIAM Review*,**42**(2000): 317-332. - [
**J18**] - “Surface Reaction Near a Stagnation Point.”
*Studies in Applied Mathematics*,**105**(2000): 1-29. - [
**J19**] - “The Effect of a Receptor Layer on the Measurement of Rate Constants.”
*Bulletin of Mathematical Biology*,**63**(2001): 301-327. - [
**J20**] - “A Spatially Nonlocal Model for Polymer-Penetrant Diffusion.”
*ZAMP*,**52**(2001): 254-288. - [
**J21**] - “A Differential Equation Model of North American Cinematic Box-Office Dynamics.”
*IMA Journal of Management Mathematics*,**12**(2001): 41-74 (with Ron A. Buckmire). - [
**J22**] - “Testing the Validity of the Effective Rate Constant Approximation for Surface Reaction with Transport.”
*Applied Mathematics Letters*,**15**(2002): 547-552 (with Seth A. Jackson). - [
**J23**] - “Desorption Overshoot in Polymer-Penetrant Systems: Asymptotic and Computational Results.”
*SIAM Journal on Applied Mathematics*,**63**(2002): 98-115 (with Richard A. Cairncross). - [
**J24**] - “Traveling Waves for Anomalous Diffusion in Polymers.”
*Applied Mathematics Letters*, 17 (2004): 7-12 (with Sumanth Swaminathan). - [
**J25**] - “Refining the Measurement of Rate Constants in the BIAcore.”
*Journal of Mathematical Biology*,**49**(2004): 272-292. - [
**J26**] - “The Effect of Receptor Site Nonuniformity on the Measurement of Rate Constants.”
*Applied Mathematics Letters*,**18**(2005): 1101-1107 (with S. Swaminathan). - [
**J27**] - “A Spatially Nonlocal Model for Polymer Desorption.”
*Journal of Engineering Mathematics*, 53 (2005): 221-238. - [
**J28**] - “Convection Effects in the BIAcore Dextran Layer: Surface Reaction Model.”
*Bulletin of Mathematical Biology*, 68 (2006): 627-654. - [
**J29**] - “Convection Effects in Thin Reaction Zones: Applications to BIAcore.”
*SIAM Journal on Applied Mathematics*,**66**(2006): 1978-1997. - [
**J30**] - “Steric Hindrance Effects on Surface Reactions: Applications to BIAcore.”
*Journal of Mathematical Biology*, 55 (2007): 517-539. - [
**J31**] - “Perturbation Approximation of Solutions of a Nonlinear Inverse Problem Arising in Olfaction Experimentation.”
*Journal of Mathematical Biology*, 55 (2007): 745-765 (with Donald A. French). - [
**J32**] - “Steric Hindrance Effects in Thin Reaction Zones: Applications to BIAcore.”
*IMA Journal of Applied Mathematics*, 72 (2007): 865-893. - [
**J33**] - “Identification of Cl(Ca) Channel Distributions in Olfactory Cilia.”
*Mathematical Methods in the Applied Sciences*, 31 (2008): 1860-1873 (with Donald A. French, Dorjsuren Badamdorj, and Steven Kleene). - [
**J34**] - “The Optimal Prepayment Strategy for Fixed Rate Mortgages.” In
*Proceedings of the World Congress on Engineering and Computer Science 2008*. (2008): 898–903 (with D. Xie and G. Schleiniger) - [
**J35**] - “An Asymptotic Method to a Financial Optimization Problem.” In
*Advances in Machine Learning and Data Analysis*, vol. 72. S. Ao,*et al.*, eds. New York: Springer (2009): 79-94 (with D. Xie and G. Schleiniger). - [
**J36**] - “Characterizing Molecular Diffusion in the Lens Capsule.”
*Matrix Biology*,**29**(2010): 228-236 (with Brian Danysh,*et al*.). - [
**J37**] - “Transport Effects on Surface Reaction Arrays: Biosensor Applications .”
*Mathematical Biosciences*,**230**(2011): 12-22. - [
**J38**] - “Characterization of the American Put Option Using Convexity.”
*Applied Mathematical Finance*,**18**(2011): 353-365 (with Dejun Xie, Gilberto Schleiniger, and Qinghua Zhu). - [
**J39**] - “Sharp Fickian Behavior of Electrogenerated Chemiluminescence Waves in Conjugated Polymer Films.”
*Journal of Physical Chemistry, Part C*,**117**(2013): 6747-6751. - [
**J40**] - “Wavefunction Delocalization in Quantum Dot Arrays: An Asymptotic Analysis.”
*Journal of Engineering Mathematics*,**81**(2013): 191-211 (with William M. Reid and Matt Doty). - [
**J41**] - “An Application of Matrix Theory to the Evolution of Coupled Modes.”
*SIAM Review*,**55**(2013): 764-787 (with Joseph Fehribach, Richard Moore, and Colin McKinstrie). - [
**J42**] - “A Mathematical Model of Cinematic Box-Office Dynamics with Geographic Effects.”
*IMA Journal of Management Mathematics*,**25**(2014): 233-257 (with Ron A. Buckmire and Jacob Ortega-Gingrich). - [
**J43**] - “Multiple Surface Reactions in Arrays with Applications to Optical Biosensors.”
*Bulletin of Mathematical Biology*,**76**(2014): 1783-1808 (with Matthew E. Zumbrum). - [
**J44**] - “Improving a Fuel Cell Assembly Process.”
*Mathematics-in-Industry Case Studies*,**6**(2014): 22-47 (with Ibrahim Diakite,*et al*.). - [
**J45**] - “Sharp Fickian Fronts in Conjugated Polymer Films.”
*IMA Journal of Applied Mathematics*,**80**(2015): 533-553. - [
**J46**] - “Conformal Mapping in Optical Biosensor Applications.”
*Journal of Mathematical Biology*,**71**(2015): 533-550 (with Matthew E. Zumbrum). - [
**J47**] - “Asymptotic Results for a Barrier Potential Model.”
*European Journal of Applied Mathematics*,**26**(2015): 863-886 (with Christopher S. Raymond). - [
**J48**] - “Modal Analysis of Spatial Pattern Formation in Fused Silica under Ultraviolet Irradiation.”
*Journal of the Optical Society of America B*,**33**(2016): 1709-1715 (with Richard Moore). - [
**J49**] - “The Performance of the Hot End in a Plasticating 3D Printer.”
*Journal of Rheology***62**(2017): 229–236 (with Michael Mackay,*et al*.). - [
**J50**] - “Applications of Fractional Calculus in Solving Abel-Type Integral Equations: Surface-Volume Reaction Problem.”
*Computers & Mathematics With Applications*,**73**(2017): 1346–1362 (with Ryan Evans, Udita Katugampola). - [
**J51**] - “Measuring Kinetic Rate Constants of Multiple-Component Reactions with Optical Biosensors.”
*Analytical Biochemistry*,**533**(2017): 41-47 (with Ryan Evans, Wenbin Li). - [
**J52**] - “Transport Effects on Multiple-Component Reactions in Optical Biosensors.”
*Bulletin of Mathematical Biology*,**79**(2017): 2215-41 (with Ryan Evans). - [
**J53**] - “Receptor Heterogeneity in Optical Biosensors.”
*Journal of Mathematical Biology*,**76**(2018): 795-816 (with Ryan Evans). - [
**J54**] - “Simulation Solution to a Two-Dimensional Mortgage Refinancing Problem.”
*Computational Economics*,**52**(2018): 479-92 (with Dejun Xie, Nan Zhang). - [
**J55**] - “An Optimal Mortgage Refinancing Strategy with Stochastic Interest Rate.”
*Computational Economics*,**53**(2019): 1353-75 (with Xiaoxia Wu, Dejun Xie). - [
**J56**] - “Maximal 3-D Printing Extrusion Rates.”
*IMA Journal of Applied Mathematics*,**84**(2019): 1022–43 (with Michael Mackay,*et al*.). - [
**J57**] - “Postextrusion Heating in Three-Dimensional Printing.”
*Journal of Heat Transfer*,**142**(2020): 052101 (9 pages) (with Michael Mackay). - [
**J58**] - “Nonisothermal Welding in Fused Filament Fabrication.”
*Additive Manufacturing*,**33**(2020): 101140 (12 pages) (with Keith Coasey,*et al*.). - [
**J59**] - “The Heat Balance Integral Method for Cylindrical Extruders.”
*Journal of Engineering Mathematics*,**122**(2020): 1-16 (with Jacob Sitison). - [
**J60**] - “Mathematical Models for the Effect of Anti-Vascular Endothelial Growth Factor on Visual Acuity.”
*Journal of Mathematical Biology*,**81**(2020): 1397-1428 (with Anna Kondic,*et al*.). - [
**J61**] - “Quasisteady Models for Weld Temperatures in Fused Filament Fabrication.”
*IMA Journal of Applied Mathematics*,**87**(2022): 292-313. - [
**J62**] - “Optimal Exercise Frontier of Bermudan Options by Simulation Methods.”
*International Journal of Financial Engineering*,**9**(2022): 2250013 (20 pages) (with Dejun Xie,*et al*.). - [
**J63**] - “Dependence of Fused Filament Fabrication Weld Strength on Experimental Parameters: A Numerical Study.”
*Journal of Manufacturing Processes*,**85**(2023): 1066-76. - [
**J64**] - “A VAR-Based Factor Decomposition to the Term Structure of Treasury Bonds.”
*International Journal of Monetary Economics and Finance*, in press (with Dejun Xie,*et al*.).

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**O1**] - “A Model for Venous Blood Flow in the Legs.”
*Mathematical Modeling: IMA Summer Program for Graduate Students*. IMA Preprint Series 1021 (1992): 31-54 (with Tara Athan [Mary Brewster],*et al*.). - [
**O2**] - “Risk Assessment for Propane Gas Leakage in Valleys.”
*Mathematical Modeling: IMA Summer Program for Graduate Students*. IMA Preprint Series 1021 (1992): 109-34 (with Tara Athan [Mary Brewster],*et al*.). - [
**O3**] - “Fluid Flow in a Filtering Device.”
*Mathematical Modeling: IMA Summer Program for Graduate Students*. IMA Preprint Series 1021 (1992): 191-221 (with Donald Drew,*et al*.). - [
**O4**] - “Flow Improvement in Hydrofractured Reservoirs.”
*Mathematical Modeling: IMA Summer Program for Graduate Students*. IMA Preprint Series 1021 (1992): 269-95 (with Pat Hagan,*et al*.). - [
**O5**] *A Model for Nonlinear Diffusion in Polymers*. Ph.D. thesis, California Institute of Technology, 1994.- [
**O6**] - “Modeling Large Gas Release Events from ‘Dry’ Waste Tanks.” In
*Proceedings of the Eleventh Workshop on Mathematical Problems in Industry*, Los Alamos Technical Report LA-UR 95-4038 (1995) (with Tara Athan [Mary Brewster],*et al*.). - [
**O7**] - “Swelling and Collapse of Elastic Shells.” Abstract. In
*Proceedings of the Twelfth International Congress on Rheology*. A. Ait-Kadi*et al*, eds. Laval University Press, Quebec (1996): 343 (with Christopher J. Durning*et al*.). - [
**O8**] - “Optimizing Membrane Separations of Two-Component Protein Solutions.” In
*Proceedings of the Twelfth Workshop on Mathematical Problems in Industry*(1996): 61-84 (with Skand Saksena,*et al*.). - [
**O9**] - “Gas Concentration Measurements in Underground Waste Storage Tanks.” In
*Proceedings of the Thirteenth Workshop on Mathematical Problems in Industry*(1997) (with Tara Athan [Mary Brewster],*et al*.). - [
**O10**] - “Theoretical Predictions of Trapping Skinning in Polymers.” Extended abstract in
*Proceedings of the Ninth International Coating Science and Technology Symposium*(1998). - [
**O11**] - “Thermomechanical Models of Air Gap Nucleation During Pure Metal Solidification on Moving Molds with Periodic Surface Topographies.” In
*Proceedings of the Fourteenth Workshop on Mathematical Problems in Industry*(1999): 11-47 (with Louis G. Hector, Jr.*et al*.). - [
**O12**] - “Interference Filters for Thermophotovoltaic Applications.” In
*Proceedings of the Fifteenth Annual Workshop on Problems in Industry*(2000) (with John Les*et al*.). - [
**O13**] - “Options on Baskets.” In
*Proceedings of the Sixteenth Workshop on Mathematical Problems in Industry*(2001) (with Pat Hagan*et al*.). - [
**O14**] - “Multi-Name Credit Derivatives.” In
*Proceedings of the Seventeenth Workshop on Mathematical Problems in Industry*(2002) (with Pat Hagan*et al*.). - [
**O15**] - “Testing the Validity of the Averaged Approximation for the IAsys.” University of Delaware Technical Report 2002-3 (2002) (with S. A. Jackson).
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**O16**] - “A Mathematical Model for Blood Clotting.” University of Delaware Technical Report 2004-04 (2004) (with S. Swaminathan).
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**O17**] - “Multi-Phase Flow in a Thin Porous Material.” In
*Proceedings of the Twentieth Workshop on Mathematical Problems in Industry*(2005) (with Uwe Beuscher*et al*.). - [
**O18**] - “Advanced Leak Detection.” In
*Proceedings of the Twenty-First Workshop on Mathematical Problems in Industry*(2006) (with R. P. Hart and D. Reicher*et al*.). - [
**O19**] - “Development of a Quaternion-Based Algorithm to Process Data in Robotics Applications.” In
*Proceedings of the Twenty-Second Workshop on Mathematical Problems in Industry*(2007) (with J. Ashmore,*et al*.). - [
**O20**] - “Characterizing Molecular Diffusion in the Lens Capsule.” In
*Proceedings of the Twenty-Third Workshop on Mathematical Problems in Industry*(2008) (with M. Duncan,*et al*.). - [
**O21**] - “Development and Persistence of ‘Static’ or ‘Dead’ Zones in Flows.” In
*Proceedings of the Twenty-Fifth Workshop on Mathematical Problems in Industry*(2009) (with J. Abbott,*et al*.). - [
**O22**] - “Medical Ultrasound Imaging.” In
*Proceedings of the Twenty-Sixth Workshop on Mathematical Problems in Industry*, (2010) (with B. Haider,*et al*.). - [
**O23**] - “Modeling Photon Generation.” In
*Proceedings of the Twenty-Seventh Workshop on Mathematical Problems in Industry*(2011) (with C. McKinstrie,*et al*.). - [
**O24**] - “Fuel Cell Assembly Process Flow for High Productivity.” In
*Proceedings of the Twenty-Eighth Workshop on Mathematical Problems in Industry*(2012) (with R. Ramanan,*et al*.). - [
**O25**] - “Phase Field Formulation for Microstructure Evolution in Oxide Ceramics.” In
*Proceedings of the Twenty-Ninth Workshop on Mathematical Problems in Industry*(2013) (with L. Button,*et al*.). - [
**O26**] - “Spatial Pattern Formation in Fused Silica Under UV Irradiation.” In
*Proceedings of the Thirtieth Workshop on Mathematical Problems in Industry*(2014) (with L. Button,*et al*.). - [
**O27**] - “Desulfurization of Natural Gas for Fuel Cells.” In
*Proceedings of the Thirty-First Workshop on Mathematical Problems in Industry*(2015) (with E. Campbell,*et al*.). - [
**O28**] - “Hybrid Programmatic TV Markets.” In
*Proceedings of the Thirty-Second Workshop on Mathematical Problems in Industry*(2016) (with M. Montes de Oca,*et al*.). - [
**O29**] - “On Characterizing and Simulating Porous Media.” In
*Proceedings of the Thirty-Third Workshop on Mathematical Problems in Industry*(2017) (with Z. He, V. Venkateshwaran,*et al*.). - [
**O30**] - “The Problem of Freezing of Copper Water Heat Pipes.” In
*Proceedings of the Thirty-Fourth Workshop on Mathematical Problems in Industry*(2018) (with J. Cepeda-Rizo,*et al*.). (also see [**O34**]) - [
**O31**] - “Parametric Models for Clinical Measurements in Ophthalmology.” In
*Proceedings of the Thirty-Fifth Workshop on Mathematical Problems in Industry*(2019) (with A. Kondic,*et al*.). - [
**O32**] - “Evaporation from Porous Media.” In
*Proceedings of the Thirty-Sixth Workshop on Mathematical Problems in Industry*(2020) (with U. Beuscher,*et al*.). - [
**O33**] - “Differential Privacy in Travel Data.” In
*Proceedings of the Thirty-Seventh Workshop on Mathematical Problems in Industry*(2021) (with J. Dumont,*et al*.). - [
**O34**] - “The Problem of Freezing of Copper Water Heat Pipes.”
*Mathematics in Industry Reports*(2021) (with S. Acharya,*et al*.). - [
**O35**] - “Parametric Models for Clinical Measurements in Ophthalmology.”
*Mathematics in Industry Reports*(2022) (with A. Kondic,*et al*.). - [
**O36**] - “Development of a Quaternion-Based Algorithm to Process Data in Robotics Applications.”
*Mathematics in Industry Reports*(2022) (with J. Ashmore, et al.). - [
**O37**] - “Finding the Limits of Machine Learning in Optimization.”
*Mathematics in Industry Reports*(2022) (with D. Kane, et al.).

Available upon request